How to implement an "unknown" class in multi-class classification with neural networks?
The usual way to implement this would be to add the new class with data examples.

Some things you need to address:


Sourcing new data for your "other" class. 
Ensuring the amount and variation of data in "other" class examples matches how the predictor will be used.


Code examples for this are not necessary, as you would just use the same network design as you already have and just add another output. This is a data and model definition problem.

Logically you have another option: As well as outputting the predicted class, you predict separately whether there is any detectable object at all as a true/false value. This still requires the additional data, but is for example how the YOLO algorithm works for object detection. Object detection has a specific meaning - it involves finding the co-ordinates and class of possibly multiple objects in an image. This goes beyond the wording of your question, but is a typical end goal if you are asking this kind of question.

YOLO predicts the presence of an object separately from the class of object. The additional data for YOLO training comes from segmenting the source images, so many parts of the target image are background with no objects. In that case the additional data you require is due to more detailed labelling within each image example.

YOLO is quite complicated architecture, so you might want to look at this example using Keras on a Github project for more details, if object detection is your goal.